Liberal arts college vs University for mathematics?

College Majors Math/Computer Science Majors
21

Note, however, that the OP will be finishing calculus BC in 11th grade and take college sophomore level math courses at a local college in 12th grade. I.e. the OP is advanced enough that s/he will go into junior level courses (theoretical linear algebra, abstract algebra, real analysis) as a college frosh.

This means that the OP will miss most of the advantages of a LAC in math (small frosh/soph level math courses) while being more likely to run into the disadvantages of a LAC in math (running out of advanced level math courses, with the exception of a few like Williams and Harvey Mudd that have more offerings including graduate level offerings).

22

What happens if I run out of classes? is something to discuss with specific schools. I suspect some will work better than others.

LACs won’t have the same breadth in the course catalog, but if the student is a good match for the faculty, there is easier access to research and independent study. Many LACs have a senior project or senior thesis that helps the student make the transition from the skills needed to be an undergrad to the skills needed for grad school.

Universities have a broader selection of classes and may have a larger faculty who cover more subfields. But one on one mentoring will require undergrads to compete for attention with grad students.

If you look at the results, both approaches can lead to PhDs, and the OP was interested in considering LACs.

23

Suggestion after helping DS and DD find their college match, and being able to help a number of other kids find their match… the learning environment in which the student feels most at home - where they find “their tribe” - is more important for success, in my opinion than just about anything.

In this particular case I would suggest looking at the LACs that graduate the most students who go on to doctorate programs as a great way to judge the list of schools you may want to consider initially.

Using WebCASPAR data, the list for doctorates in mathematics starts with these (beginning with the top ranked LAC):

Pomona
St Olaf
Williams
Carlton
Smith
Amherst

Etc…

This is a list by total count; you can also find lists that run results on a per capital basis. That is useful too, but I would argue tips the scale towards small colleges.

All I am arguing is to use lists like these to narrow the initial search and then go visit and see where the fit feels right. It is hard to excel academically if you don’t connect with the other students.

24

Definitely check out Pomona- the 5C’s give you a huge depth of math courses (you can take advanced courses at CGU as well), and most of my friends who majored in math are attending top graduate schools (Berkeley, Stanford, Carnegie Mellon, Princeton, etc). It is also the second most popular major at the college.

25

You can find a full listing of all Claremont College math courses here: http://ccms.claremont.edu/Claremont_Math_Classes

Math is an intercollegiate department, so there are no restrictions in which you can take or how many you can take. I’ve never seen an advanced math class being restricted to only students from one college.

26

Okay, on a general note:

One thing to recognize is that there’s a pure and applied math division; pure math is much more selective.

If you want to go to a top 5 pure math school, keep in mind you’re competing with people who’ve done math and math only for their whole lives. They were USAMO/International Mathematical Olympiad winners in high schools, and they go to top colleges and begin their coursework in graduate level courses. They are the ones who score the highest on the Putnam exams and win the Morgan Prize for outstanding math research (or an honorable mention) as an undergrad. Virtually all of them go onto graduate programs- they are the ones who represent the top programs. The only LAC which has been seen in those prestigious awards is Harvey Mudd, and only 1-3 times in a 20 year period. In fact, beyond maybe 5 or 6 schools, you won’t see much representation for the top scorers among universities or LACs. Furthermore, you not only have to be a math student at those other schools, but the top student for several years. Among the highest performing universities, you have to be one of the top 10-20 math students among hundreds of majors. The average math major at any school- and that includes Harvard/MIT/etc.- is nowhere near there. If you’re at the level to be admitted to a top 5 pure math school, you will be at the level to be admitted to the top undergrad programs, too.

This is something we folk at LACs are warned about- and this is true not just for Pomona and Swarthmore, but Williams and Harvey Mudd too. The LACs are filled with bright students, but few of the extraordinary ones; the top universities are similar, but with more extraordinary kids. You can do everything perfectly at the LACs- graduate summa cum laude, do research every year, be published, and you still won’t be admitted to a top pure math grad school. Case in point- 2 of my friends who are now attending Berkeley for pure math PhD, who did all that, did the Budapest semesters in math, and were not admitted to any other top 5 program. It’s not because LAC grads are looked down upon, it’s because they’re not competitive with the extraordinary students at the top US universities and abroad (IIT/Waterloo/Oxford/etc.).

Graduate school admissions has gotten more selective in recent years. The reason Swarthmore is not sending graduates to top 5 pure math programs on a consistent basis, and I’m fairly sure this certain of Williams and Mudd too- is because of that trend. You could be a top, but not extraordinary, student in past years and get into top 5 programs. But now there are more and more top/extraordinary students around the world such that LAC top grads are being blocked out by the programs.

If you want to do applied math or are fine with a pure math PhD from a school not ranked in the top 5, getting into a top PhD program from a LAC is not as difficult. The extraordinary kids at the universities aren’t as interested in applied math. We were encouraged at Pomona to do the stats/applied track of the major if we were interested in going to a tippy top grad school; the students who were admitted to Stanford/Princeton/Carnegie Mellon/Cornell/Harvard were all applied or stats majors. In fact, the only top 5 pure math program I’ve heard of a Pomona student getting into for the last 3 years is Berkeley.

It is not the institution which will decide your outcomes, but what you yourself do. Going to a LAC can still position you to a top grad program, but you will find a greater depth of courses, research, and extraordinary peers at the best universities.

27

From my limited experience, at least with the courses I took with these people, these people aren’t some people that are in some different pedestal.
Most of them feel like ordinary human beings and you wouldn’t know they won all these prizes and stuffs until you are notified.
(And many of them don’t start their coursework in grad level courses. Competition math is different from school math)

What I am trying to state is that at least when taking the same courses as students like them, one shouldn’t fret about much.
These people are normal human beings too. Just normal human beings with a strong work ethic.
So don’t fret too much thinking of all these ‘world rank’ students. They are just everyday people like you (in the fact that when they are learning something new like you, they are going to be “learning” with you. They will struggle just as much, etc. so it’s not much of a disadvantage at least in terms of coursework. Now in terms of competition math, they tend to be leagues above (since they have been practicing for a large portion of their lives on it))

And as for what @nostalgicwisdom had said.
Pure Math is an EXTREMELY selective field especially at the top 5. Princeton Univ pure math? Even a near 4.3 from CalTech does not guarantee at all from what I have heard.
Pure Math tends to be more selective than Applied Math for sure. But don’t let that discourage you.
There are indeed so many more schools than just 5 in the world.
That said, if you want to get into the top of the top grad schools for pure math, then you ‘kind of’ have to attend a university. There really isn’t much of an option from what I see.

28

Bowdoin, Carleton, Grinnell, Hamilton, Harvey Mudd, Haverford, Macalester and Reed are the highly selective LACs that appear in a Princeton Review sampling, “Great Schools for Mathematics Majors.” Beyond proof-based linear algebra (the standard “gateway” college mathematics course), it would appear that you would have about 16 additional math courses to choose from at some of these colleges, plus the option of a Budapest semester. The point at which you anticipate entering this sequence would determine the adequacy of the math curricula at these schools. That is, the further beyond linear algebra you have progressed as a pre-college student, the fewer your math course options would be at these particular schools. Note, however, that more than half of your courses would be recommended (or required) to be outside of your major at a liberal arts college, so the maximum amount of math courses that you would take in any event would seem to be about fifteen.

29

In the interest of maintaining confidentiality, let’s just say I’m a tenured professor at a top liberal arts college, and was previously on the faculty at a state flagship, so can speak to the learning environment at a few kinds of institution.

OP: Having taken Calculus BC as a junior means your background is stronger than average, but wouldn’t be all that unusual at my institution or any of those mentioned above. Depending on what you decide to do next year you would likely begin with an “early intermediate” course like linear algebra, and wouldn’t run out of courses.

That said, I’ll give you a bit of advice that I like to give my students: you should conduct your education as if you will run out of courses. By that I mean your goal in learning mathematics should first and foremost be intellectual independence and self-sufficiency. Students who truly achieve those goals are the best qualified for graduate study in mathematics, regardless of the fancy list of courses they’ve been attending.

It is a bit premature to be having the “top graduate school” discussion. Despite what other posters seem to believe, there is no undergraduate institution that will, on its own, either ensure or prevent admission to a pure math PhD program. Far more important is the quality of work that you do, and your development as a learner of mathematics. Why would access to graduate courses at Harvard matter if you are unhappy with the learning environment, and therefore not doing your best work? How much would the small classes and personal attention at Williams benefit you if you’re unhappy (say) with the isolation of a rural environment? It’s quite hard to compare institutions against each other in an “all else being equal” exercise, when all else is almost never equal.

A great many liberal arts colleges and smaller universities have been mentioned above where you would be well-served. As for specific suggestions off the top of my head:

Any of the upper tier of LAC would be great, a few especially successful programs are: Bowdoin, Carleton, St. Olaf, Williams, Swarthmore, Kenyon, Smith.

Some smaller universities with strong undergraduate programs: Vanderbilt, Wash U St. Louis, Rice, Dartmouth.

Some great state flagships with strong undergraduate math programs: UVA, U Wisconsin, U Texas at Austin.

You may be surprised to learn that, within mathematics departments, you’ll find more similarities than differences in the undergraduate experience among these various institutions. I encourage you primarily to seek out the kind of learning environment that suits you best, in the sort of place where you’ll be most content and ready to do your best work. From there, you can make fine distinctions about curriculum and how best to pursue your post-graduate goals. All of the institutions in the range you are considering will be fine choices from a purely academic point of view.

30

What was the context of that information. If fewer math students are going on to top 5 grad schools it may well be that: 1. they are being lured directly into the workforce with high starting salaries, or 2. they are choosing other grad schools which, while not arbitrarily ranked as “top 5” are actually doing better and more interesting work.

If fewer Swat grads are going into specific programs, it may be because they’re casting their nets in other directions.